Question $2$: $[15$ points$]$ Assume that you are a CPEG student and you are hired as an

intern by Arman for his hardware company that only utilizes NOR $(\frac{?}{\text{b}\text{a}\text{r}}(grad))$

gates for logic operations. NOR gate is implemented as $\frac{p}{b}ar(vv)q=$not$(pvvq).$

Recall that the OR gate for inputs $p,q$ is calculated as $pvvq.$ NOT gate

of $p$ is calculated as notp and the AND gate of inputs $p,q$ is calculated as

$p^{{?}^{?}}q.$

$($a$)[6$ points